Subgroups — #10588685⋊C₃ #13142710

Order 1728.

500 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3697⋊C₃	C₂	1	1	yes	maximal, characteristic
2	3₋¹⁺²×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#3667⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#63364⋊C₃	C₂	1	4	yes	maximal, complemented
5	C₃×#5005	—	3	1	no	maximal
6	#10588685	C₃	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
8	C₂×#611⋊C₃	—	2	1	no	—
9	#3697⋊C₃	—	2	1	no	—
10	#3697⋊C₃	—	2	1	no	—
11	#3697⋊C₃	C₄	1	2	yes	complemented
12	#3697⋊C₃	C₂²	1	2	yes	—
13	C₂×C₄⋊AGL(1,ℤ/9)	C₄	1	1	yes	characteristic, complemented
14	C₂×C₄×AGL(1,ℤ/9)	—	2	1	no	—
15	C₂×3₋¹⁺²⋊Q₈	C₄	1	1	yes	characteristic, complemented
16	C₄⋊C₄×3₋¹⁺²	—	2	1	no	—
17	C₂²⋊C₄×3₋¹⁺²	—	2	1	no	—
18	C₄²×3₋¹⁺²	C₂²	1	2	yes	complemented
19	#3667⋊C₃	—	2	1	no	—
20	#3667⋊C₃	C₂²	1	2	yes	complemented
21	C₂×3₋¹⁺²⋊C₈	—	2	1	no	—
22	C₂×C₃×#235	—	3	1	no	—
23	C₃²×#117	D₃	1	1	yes	characteristic
24	C₂×C₃×#208	—	3	1	no	—
25	C₂×#3697	C₂×C₃	1	1	yes	characteristic
26	C₃×#805	—	3	4	no	—
27	C₉×#117	—	2	1	no	—
28	C₉×#117	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×#3667	C₂×C₃	1	1	yes	characteristic, complemented
30	#63364	C₂×C₃	1	4	yes	complemented
31	C₂³×3₋¹⁺²	D₄	1	1	yes	characteristic
32	C₂²×AGL(1,ℤ/9)	—	2	1	no	—
33	C₂×C₄×3₋¹⁺²	—	2	2	no	—
34	C₂×C₄×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄×3₋¹⁺²	D₄	1	1	yes	characteristic
37	C₂×C₄×3₋¹⁺²	D₄	1	1	yes	characteristic
38	C₂×C₄×3₋¹⁺²	D₄	1	1	yes	characteristic
39	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
40	#611⋊C₃	—	2	2	no	—
41	#611⋊C₃	—	2	2	no	—
42	C₂×3₋¹⁺²⋊C₄	—	2	1	no	—
43	C₄⋊AGL(1,ℤ/9)	—	2	1	no	—
44	C₄⋊AGL(1,ℤ/9)	C₂×C₄	1	2	yes	—
45	C₄×AGL(1,ℤ/9)	—	2	2	no	—
46	C₄×AGL(1,ℤ/9)	—	2	2	no	—
47	3₋¹⁺²⋊Q₈	—	2	1	no	—
48	3₋¹⁺²⋊Q₈	C₂×C₄	1	2	yes	—
49	3₋¹⁺²⋊C₈	—	2	2	no	—
50	C₃×#421	—	9	1	no	—
51	#5005	—	3	1	no	—
52	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
53	C₂×C₃×#67	—	6	1	no	—
54	C₃×#235	—	3	2	no	—
55	C₃×#235	—	3	2	no	—
56	C₃×#235	—	6	1	no	—
57	C₃×#235	—	6	1	no	—
58	C₂×C₃×D₁₂	—	3	1	no	—
59	C₂×C₃×C₄×D₃	—	6	1	no	—
60	C₂×C₃×Dic₆	—	3	1	no	—
61	C₃²×C₄⋊C₄	—	2	1	no	—
62	C₃²×C₂²⋊C₄	—	2	1	no	—
63	C₃²×C₄²	C₂×D₃	1	2	yes	—
64	C₃×#208	—	3	2	no	—
65	C₃×#208	—	6	1	no	—
66	C₂×C₃×C₃⋊C₈	—	6	1	no	—
67	C₂²×C₄×C₉	—	2	1	no	—
68	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
69	C₂×#611	—	2	1	no	—
70	#3697	—	2	1	no	—
71	#3697	—	2	1	no	—
72	#3697	C₃×C₄	1	2	yes	complemented
73	#3697	C₂²×C₃	1	2	yes	—
74	C₂×D₃₆	C₃×C₄	1	1	yes	characteristic, complemented
75	C₂×C₄×D₉	—	2	1	no	—
76	C₂×Dic₁₈	C₃×C₄	1	1	yes	characteristic, complemented
77	C₉×C₄⋊C₄	—	2	2	no	—
78	C₉×C₄⋊C₄	—	2	1	no	—
79	C₉×C₂²⋊C₄	—	2	2	no	—
80	C₉×C₂²⋊C₄	—	2	1	no	—
81	C₄²×C₉	—	2	2	no	—
82	C₄²×C₉	C₂²×C₃	1	2	yes	complemented
83	#3667	—	2	1	no	—
84	#3667	C₂²×C₃	1	2	yes	complemented
85	C₂×C₉⋊C₈	—	2	1	no	—
86	C₂²×3₋¹⁺²	—	4	1	no	—
87	C₂²×3₋¹⁺²	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×3₋¹⁺²	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
90	C₂×AGL(1,ℤ/9)	—	2	2	no	—
91	C₂×AGL(1,ℤ/9)	—	4	2	no	—
92	C₄×3₋¹⁺²	—	4	2	no	—
93	C₄×3₋¹⁺²	C₂²⋊C₄	1	1	yes	characteristic
94	C₄×3₋¹⁺²	C₂²⋊C₄	1	1	yes	characteristic
95	C₄×3₋¹⁺²	C₂²×C₄	1	1	yes	characteristic
96	C₄×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
97	3₋¹⁺²⋊C₄	—	2	2	no	—
98	C₂×C₃×#41	—	9	1	no	—
99	C₂×#235	—	3	1	no	—
100	C₂×C₃×M₁₆	—	9	1	no	—
101	C₃×#117	—	3	1	no	—
102	C₃×#117	C₃×D₃	1	1	yes	characteristic
103	C₂×#208	—	3	1	no	—
104	C₃×#104	—	9	4	no	—
105	#805	—	3	4	no	—
106	C₂³×C₃²	#67	1	1	yes	characteristic
107	C₂²×C₃×D₃	—	6	1	no	—
108	C₂×C₃²×C₄	—	2	2	no	—
109	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
110	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
111	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
112	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
113	C₂×C₃²×C₄	#67	1	1	yes	characteristic
114	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
115	C₃×#67	—	6	2	no	—
116	C₃×#67	—	6	2	no	—
117	C₂×C₃×Dic₃	—	6	1	no	—
118	C₃×D₁₂	—	3	2	no	—
119	C₃×D₁₂	—	6	1	no	—
120	C₃×C₄×D₃	—	6	2	no	—
121	C₃×C₄×D₃	—	6	2	no	—
122	C₃×Dic₆	—	3	2	no	—
123	C₃×Dic₆	—	6	1	no	—
124	C₂³×C₉	—	2	1	no	—
125	C₂³×C₉	C₃×D₄	1	1	yes	characteristic
126	C₂²×D₉	—	2	1	no	—
127	C₃×C₃⋊C₈	—	6	2	no	—
128	C₂×C₄×C₉	—	2	4	no	—
129	C₂×C₄×C₉	—	2	2	no	—
130	C₂×C₄×C₉	—	2	1	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	2	1	no	—
133	C₂×C₄×C₉	—	2	1	no	—
134	C₂×C₄×C₉	—	2	1	no	—
135	C₂×C₄×C₉	—	2	1	no	—
136	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
137	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
138	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
139	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
140	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
141	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
142	#611	—	2	2	no	—
143	#611	—	2	2	no	—
144	C₂×Dic₉	—	2	1	no	—
145	D₃₆	—	2	1	no	—
146	D₃₆	C₂×C₃×C₄	1	2	yes	—
147	C₄×D₉	—	2	2	no	—
148	C₄×D₉	—	2	2	no	—
149	Dic₁₈	—	2	1	no	—
150	Dic₁₈	C₂×C₃×C₄	1	2	yes	—
151	C₉⋊C₈	—	2	2	no	—
152	#421	—	9	1	no	Sylow
153	C₂×3₋¹⁺²	—	2	1	no	—
154	C₂×3₋¹⁺²	—	2	1	no	—
155	C₂×3₋¹⁺²	—	2	1	no	—
156	C₂×3₋¹⁺²	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	AGL(1,ℤ/9)	—	4	2	no	—
158	C₃×#41	—	9	2	no	—
159	C₃×#41	—	9	2	no	—
160	C₃×#41	—	18	1	no	—
161	C₃×#41	—	18	1	no	—
162	C₂×C₃×Q₈	—	9	1	no	—
163	C₂×C₃×D₄	—	9	1	no	—
164	C₂×C₃×D₄	—	18	1	no	—
165	C₂²×C₃×C₄	—	3	1	no	—
166	C₂²×C₃×C₄	—	18	1	no	—
167	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
168	C₂×#67	—	6	1	no	—
169	#235	—	3	2	no	—
170	#235	—	3	2	no	—
171	#235	—	6	1	no	—
172	#235	—	6	1	no	—
173	C₂×D₁₂	—	3	1	no	—
174	C₂×C₄×D₃	—	6	1	no	—
175	C₂×Dic₆	—	3	1	no	—
176	C₃×M₁₆	—	9	2	no	—
177	C₃×M₁₆	—	18	1	no	—
178	C₂×C₃×C₈	—	18	1	no	—
179	C₃×C₄⋊C₄	—	2	1	no	—
180	C₃×C₄⋊C₄	—	6	1	no	—
181	C₃×C₂²⋊C₄	—	2	1	no	—
182	C₃×C₂²⋊C₄	—	6	1	no	—
183	C₃×C₄²	—	3	2	no	—
184	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
185	#208	—	3	2	no	—
186	#208	—	6	1	no	—
187	C₂×C₃⋊C₈	—	6	1	no	—
188	C₂²×C₃²	—	4	1	no	—
189	C₂²×C₃²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
190	C₂²×C₃²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
191	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
192	C₂×C₃×D₃	—	6	2	no	—
193	C₂×C₃×D₃	—	12	2	no	—
194	C₃²×C₄	—	4	2	no	—
195	C₃²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
196	C₃²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
197	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
198	C₃²×C₄	C₂×D₁₂	1	1	yes	characteristic
199	C₃×Dic₃	—	6	2	no	—
200	C₂²×C₉	—	2	1	no	—
201	C₂²×C₉	—	2	1	no	—
202	C₂²×C₉	—	2	1	no	—
203	C₂²×C₉	—	4	1	no	—
204	C₂²×C₉	—	4	2	no	—
205	C₂²×C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
206	C₂²×C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
207	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
208	C₂×D₉	—	2	2	no	—
209	C₂×D₉	—	4	2	no	—
210	C₄×C₉	—	2	1	no	—
211	C₄×C₉	—	2	1	no	—
212	C₄×C₉	—	2	1	no	—
213	C₄×C₉	—	2	1	no	—
214	C₄×C₉	—	4	4	no	—
215	C₄×C₉	—	4	2	no	—
216	C₄×C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
217	C₄×C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
218	C₄×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
219	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
220	Dic₉	—	2	2	no	—
221	C₂×#41	—	9	1	no	—
222	C₂×M₁₆	—	9	1	no	—
223	#117	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
224	#104	—	9	4	no	—
225	3₋¹⁺²	#421	1	1	yes	characteristic, complemented, Sylow
226	C₂³×C₃	—	3	1	no	—
227	C₂³×C₃	—	18	1	no	—
228	C₂³×C₃	C₃×#67	1	1	yes	characteristic
229	C₂²×D₃	—	6	1	no	—
230	C₃×Q₈	—	9	2	no	—
231	C₃×Q₈	—	18	1	no	—
232	C₃×D₄	—	9	2	no	—
233	C₃×D₄	—	18	1	no	—
234	C₃×D₄	—	18	2	no	—
235	C₃×D₄	—	18	2	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	3	1	no	—
238	C₂×C₃×C₄	—	3	1	no	—
239	C₂×C₃×C₄	—	3	1	no	—
240	C₂×C₃×C₄	—	3	1	no	—
241	C₂×C₃×C₄	—	3	1	no	—
242	C₂×C₃×C₄	—	3	1	no	—
243	C₂×C₃×C₄	—	6	2	no	—
244	C₂×C₃×C₄	—	18	2	no	—
245	C₂×C₃×C₄	—	18	2	no	—
246	C₂×C₃×C₄	—	18	1	no	—
247	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
248	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
249	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
250	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
251	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
253	#67	—	6	2	no	—
254	#67	—	6	2	no	—
255	C₂×Dic₃	—	6	1	no	—
256	D₁₂	—	3	2	no	—
257	D₁₂	—	6	1	no	—
258	C₄×D₃	—	6	2	no	—
259	C₄×D₃	—	6	2	no	—
260	Dic₆	—	3	2	no	—
261	Dic₆	—	6	1	no	—
262	C₃×C₈	—	18	2	no	—
263	C₃⋊C₈	—	6	2	no	—
264	C₂×C₃²	—	2	1	no	—
265	C₂×C₃²	—	2	1	no	—
266	C₂×C₃²	—	2	1	no	—
267	C₂×C₃²	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
268	C₃×D₃	—	12	2	no	—
269	C₂×C₉	—	2	2	no	—
270	C₂×C₉	—	2	1	no	—
271	C₂×C₉	—	2	1	no	—
272	C₂×C₉	—	2	1	no	—
273	C₂×C₉	—	2	1	no	—
274	C₂×C₉	—	4	1	no	—
275	C₂×C₉	—	4	1	no	—
276	C₂×C₉	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
277	D₉	—	4	2	no	—
278	#41	—	9	2	no	—
279	#41	—	9	2	no	—
280	#41	—	18	1	no	—
281	#41	—	18	1	no	—
282	C₂×Q₈	—	9	1	no	—
283	C₂×D₄	—	9	1	no	—
284	C₂×D₄	—	18	1	no	—
285	C₂²×C₄	—	18	1	no	—
286	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
287	M₁₆	—	9	2	no	—
288	M₁₆	—	18	1	no	—
289	C₂×C₈	—	18	1	no	—
290	C₄⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	2	1	no	—
292	C₄²	C₂×AGL(1,ℤ/9)	1	2	yes	complemented
293	C₂²×C₃	—	3	1	no	—
294	C₂²×C₃	—	3	1	no	—
295	C₂²×C₃	—	3	1	no	—
296	C₂²×C₃	—	4	1	no	—
297	C₂²×C₃	—	12	1	no	—
298	C₂²×C₃	—	18	2	no	—
299	C₂²×C₃	—	36	2	no	—
300	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
301	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
302	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
303	C₂×D₃	—	6	2	no	—
304	C₂×D₃	—	12	2	no	—
305	C₃×C₄	—	3	1	no	—
306	C₃×C₄	—	3	1	no	—
307	C₃×C₄	—	3	1	no	—
308	C₃×C₄	—	3	1	no	—
309	C₃×C₄	—	4	2	no	—
310	C₃×C₄	—	12	2	no	—
311	C₃×C₄	—	18	2	no	—
312	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
313	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
314	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
315	C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
316	Dic₃	—	6	2	no	—
317	C₃²	#5005	1	1	yes	characteristic
318	C₉	—	2	1	no	—
319	C₉	C₃×#421	1	1	yes	characteristic, complemented
320	C₂³	—	18	1	no	—
321	C₂³	#611⋊C₃	1	1	yes	characteristic
322	Q₈	—	9	2	no	—
323	Q₈	—	18	1	no	—
324	D₄	—	9	2	no	—
325	D₄	—	18	2	no	—
326	D₄	—	18	2	no	—
327	D₄	—	18	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	18	1	no	—
330	C₂×C₄	—	18	2	no	—
331	C₂×C₄	—	18	2	no	—
332	C₂×C₄	C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
333	C₂×C₄	C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
334	C₂×C₄	C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
335	C₂×C₄	C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
336	C₂×C₄	#611⋊C₃	1	1	yes	characteristic
337	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
338	C₈	—	18	2	no	—
339	C₂×C₃	—	2	1	no	—
340	C₂×C₃	—	2	1	no	—
341	C₂×C₃	—	2	1	no	—
342	C₂×C₃	—	3	1	no	—
343	C₂×C₃	—	6	1	no	—
344	C₂×C₃	—	6	1	no	—
345	C₂×C₃	—	6	1	no	—
346	C₂×C₃	—	36	2	no	—
347	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
348	D₃	—	12	2	no	—
349	C₂²	—	4	1	no	—
350	C₂²	—	18	2	no	—
351	C₂²	—	36	2	no	—
352	C₂²	(C₂×AGL(1,ℤ/9))⋊C₄	1	1	yes	characteristic
353	C₂²	(C₂×AGL(1,ℤ/9))⋊C₄	1	1	yes	characteristic
354	C₂²	C₂×#611⋊C₃	1	1	yes	characteristic
355	C₄	—	4	2	no	—
356	C₄	—	18	2	no	—
357	C₄	(C₂×AGL(1,ℤ/9))⋊C₄	1	1	yes	characteristic
358	C₄	(C₂×AGL(1,ℤ/9))⋊C₄	1	1	yes	characteristic
359	C₄	C₂×C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
360	C₄	C₂×C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
361	C₃	—	3	1	no	—
362	C₃	C₃×#5005	1	1	yes	characteristic
363	C₂	—	2	1	no	—
364	C₂	—	2	1	no	—
365	C₂	—	2	1	no	—
366	C₂	—	36	2	no	—
367	C₂	C₂×(C₂×AGL(1,ℤ/9))⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×C₄⋊AGL(1,ℤ/9)
commutator	C₄×C₉	C₂²×C₃×C₄
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	3₋¹⁺²×#117	C₂
socle	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄
prime radical	C₂×#3697⋊C₃	C₂
cosocle	C₂×C₄×C₉	C₂³×C₃
hypercenter	#117	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#421
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #117

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. 3₋¹⁺²×#117	C₂	semidirect
3. C₂×#3667⋊C₃	C₂	semidirect
4. #63364⋊C₃	C₂	semidirect
6. #10588685	C₃	semidirect
11. #3697⋊C₃	C₄	semidirect
13. C₂×C₄⋊AGL(1,ℤ/9)	C₄	semidirect
15. C₂×3₋¹⁺²⋊Q₈	C₄	semidirect
18. C₄²×3₋¹⁺²	C₂²	semidirect
20. #3667⋊C₃	C₂²	semidirect
28. C₉×#117	C₂×C₃	semidirect
29. C₂×#3667	C₂×C₃	semidirect
30. #63364	C₂×C₃	semidirect
72. #3697	C₃×C₄	semidirect
74. C₂×D₃₆	C₃×C₄	semidirect
76. C₂×Dic₁₈	C₃×C₄	semidirect
82. C₄²×C₉	C₂²×C₃	semidirect
84. #3667	C₂²×C₃	semidirect
223. #117	AGL(1,ℤ/9)	semidirect
225. 3₋¹⁺²	#421	semidirect
292. C₄²	C₂×AGL(1,ℤ/9)	semidirect
319. C₉	C₃×#421	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#3697⋊C₃	2
3₋¹⁺²×#117	2
C₂×#3667⋊C₃	2
#63364⋊C₃	2
C₃×#5005	3
#10588685	3

Subgroups — #10588685⋊C3 #13142710

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10588685⋊C₃ #13142710